I'll 2nd the Two Wheel Inn. They cater to motorcyclists heavily. They also have a big garage and lots of tools in case you need to repair your bike but Wheeler's Garage is THE guy to get you out of a jam... he can fab anything on the spot.
Mid-week is choice and least busy. What makes the Dragon so popular is not onlt because it is highly technical but there are no driveways and no concerns of cars pulling out in front of you. BUT, it doesn't mean you won't meet a car of bike in your lane along the way.
Lots of awesome roads to travel there. If you do the Cherohala Skyway (which is a great high-speed run with long sweepers) please be VERY careful of the big diminishing radius corner. A lot have crashed, lost limbs and lost lives on that one corner. Find it and get to know it before speeding through it.
Rt 28 is one of my favorites... very technical but you need to be aware of residents there.
I'd recommend going slower through any of it the first time and work on a faster run later. Gives you a chance to look for the LEOs first.
Have an AWESOME and SAFE trip!